

'''simple docstring'''
import heapq


def  a__       (    _SCREAMING_SNAKE_CASE   :       dict				)     ->					set[int]:


	"""simple docstring"""





	UpperCAmelCase_     :      list[list]						=  []

	# for each node and his adjacency list add them and the rank of the node to queue
	# using heapq module the queue will be filled like a Priority Queue
	# heapq works with a min priority queue, so I used -1*len(v) to build it
	for key, value in graph.items():
		# O(log(n))
		heapq.heappush(_SCREAMING_SNAKE_CASE	,				[-1 * len(_SCREAMING_SNAKE_CASE				), (key, value)]				)

	# chosen_vertices = set of chosen vertices
	UpperCAmelCase_     :      Optional[int]						=  set()

	# while queue isn't empty and there are still edges
	#   (queue[0][0] is the rank of the node with max rank)
	while queue and queue[0][0] != 0:
		# extract vertex with max rank from queue and add it to chosen_vertices
		UpperCAmelCase_     :      Tuple						=  heapq.heappop(_SCREAMING_SNAKE_CASE				)[1][0]
		chosen_vertices.add(_SCREAMING_SNAKE_CASE				)

		# Remove all arcs adjacent to argmax
		for elem in queue:
			# if v haven't adjacent node, skip
			if elem[0] == 0:
				continue
			# if argmax is reachable from elem
			# remove argmax from elem's adjacent list and update his rank
			if argmax in elem[1][1]:
				UpperCAmelCase_     :      Any						=  elem[1][1].index(_SCREAMING_SNAKE_CASE				)
				del elem[1][1][index]
				elem[0] += 1
        # re-order the queue
		heapq.heapify(_SCREAMING_SNAKE_CASE				)
	return chosen_vertices


if __name__ == "__main__":
					import doctest

					doctest.testmod()

					_lowerCamelCase      					=     {0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
					print(f"""Minimum vertex cover:\n{greedy_min_vertex_cover(graph)}""")












"""simple docstring"""





from scipy.stats import pearsonr

import datasets


_SCREAMING_SNAKE_CASE   :							List[str]          =		'''
Pearson correlation coefficient and p-value for testing non-correlation.
The Pearson correlation coefficient measures the linear relationship between two datasets. The calculation of the p-value relies on the assumption that each dataset is normally distributed. Like other correlation coefficients, this one varies between -1 and +1 with 0 implying no correlation. Correlations of -1 or +1 imply an exact linear relationship. Positive correlations imply that as x increases, so does y. Negative correlations imply that as x increases, y decreases.
The p-value roughly indicates the probability of an uncorrelated system producing datasets that have a Pearson correlation at least as extreme as the one computed from these datasets.
'''


_SCREAMING_SNAKE_CASE   :							int          =		'''
Args:
    predictions (`list` of `int`): Predicted class labels, as returned by a model.
    references (`list` of `int`): Ground truth labels.
    return_pvalue (`boolean`): If `True`, returns the p-value, along with the correlation coefficient. If `False`, returns only the correlation coefficient. Defaults to `False`.

Returns:
    pearsonr (`float`): Pearson correlation coefficient. Minimum possible value is -1. Maximum possible value is 1. Values of 1 and -1 indicate exact linear positive and negative relationships, respectively. A value of 0 implies no correlation.
    p-value (`float`): P-value, which roughly indicates the probability of an The p-value roughly indicates the probability of an uncorrelated system producing datasets that have a Pearson correlation at least as extreme as the one computed from these datasets. Minimum possible value is 0. Maximum possible value is 1. Higher values indicate higher probabilities.

Examples:

    Example 1-A simple example using only predictions and references.
        >>> pearsonr_metric = datasets.load_metric("pearsonr")
        >>> results = pearsonr_metric.compute(predictions=[10, 9, 2.5, 6, 4], references=[1, 2, 3, 4, 5])
        >>> print(round(results[\'pearsonr\'], 2))
        -0.74

    Example 2-The same as Example 1, but that also returns the `p-value`.
        >>> pearsonr_metric = datasets.load_metric("pearsonr")
        >>> results = pearsonr_metric.compute(predictions=[10, 9, 2.5, 6, 4], references=[1, 2, 3, 4, 5], return_pvalue=True)
        >>> print(sorted(list(results.keys())))
        [\'p-value\', \'pearsonr\']
        >>> print(round(results[\'pearsonr\'], 2))
        -0.74
        >>> print(round(results[\'p-value\'], 2))
        0.15
'''


_SCREAMING_SNAKE_CASE   :							Dict          =		'''
@article{2020SciPy-NMeth,
author  = {Virtanen, Pauli and Gommers, Ralf and Oliphant, Travis E. and
      Haberland, Matt and Reddy, Tyler and Cournapeau, David and
      Burovski, Evgeni and Peterson, Pearu and Weckesser, Warren and
      Bright, Jonathan and {van der Walt}, St{\'e}fan J. and
      Brett, Matthew and Wilson, Joshua and Millman, K. Jarrod and
      Mayorov, Nikolay and Nelson, Andrew R. J. and Jones, Eric and
      Kern, Robert and Larson, Eric and Carey, C J and
      Polat, Ilhan and Feng, Yu and Moore, Eric W. and
      {VanderPlas}, Jake and Laxalde, Denis and Perktold, Josef and
      Cimrman, Robert and Henriksen, Ian and Quintero, E. A. and
      Harris, Charles R. and Archibald, Anne M. and
      Ribeiro, Antonio H. and Pedregosa, Fabian and
      {van Mulbregt}, Paul and {SciPy 1.0 Contributors}},
title   = {{{SciPy} 1.0: Fundamental Algorithms for Scientific
      Computing in Python}},
journal = {Nature Methods},
year    = {2020},
volume  = {17},
pages   = {261--272},
adsurl  = {https://rdcu.be/b08Wh},
doi = {10.1038/s41592-019-0686-2},
}
'''






@datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION    , _KWARGS_DESCRIPTION						)
class 	a		(   datasets.Metric						):






    def   UpperCamelCase			(			self	:				Dict   )	->						Any:
      return datasets.MetricInfo(
          description=_DESCRIPTION			,		citation=_CITATION			,		inputs_description=_KWARGS_DESCRIPTION			,		features=datasets.Features(
              {
                  'predictions': datasets.Value('float'   ),
                  'references': datasets.Value('float'   ),
              }   )			,		reference_urls=['https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.pearsonr.html']			,		)






    def   UpperCamelCase			(			self	:				Union[str, Any]			,		__SCREAMING_SNAKE_CASE	:				List[Any]			,		__SCREAMING_SNAKE_CASE	:				Tuple			,		__SCREAMING_SNAKE_CASE	:				Tuple=False   )	->						Tuple:
      if return_pvalue:
        lowerCamelCase_       	=		pearsonr(__SCREAMING_SNAKE_CASE			,		__SCREAMING_SNAKE_CASE   )
        return {"pearsonr": results[0], "p-value": results[1]}
      else:
        return {"pearsonr": float(pearsonr(__SCREAMING_SNAKE_CASE			,		__SCREAMING_SNAKE_CASE   )[0]   )}




